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# Where does idea of infinite size of universe come from?

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2 minutes ago, Gfamily said:

I would say that adding a boundary to the Universe adds complexity. What does it even mean for a universe to have a boundary?

There is no evidence for a boundary anywhere that we can observe - surely that is where Occam's razor should be applied.

No one mentioned boundary.

There is distinction between "bounded" geometry and one with boundary.

Bounded simply means finite in extent in sense that distance between any two points in space is less than some particular number associated with geometry. It does not imply boundary. Maybe best way to explain it would be 1d case.

Let's look at straight line that goes off to infinity. Now we are not considering "boundary" of such line with respect to higher dimensions that we embed geometry in - we don't think that line has boundary with respect to paper that it is draw on, nor in 2d/3d space that we imagine it in. We define boundary as place where one can't move further in given direction as there is no "next" point. With line we only have two directions - left and right or "up/down the line".

With straight line you can choose two points to be further away than any given distance. Line is unbounded in this sense.

Now let's consider circle with finite radius, again only directions are "up/down" the circle, or clockwise / anticlockwise. Again such geometry does not have a boundary, but it is bounded. Pick any two points on the circle and they will be closer than (2r+1)*pi where r is radius of this circle.

That is what bounded means - there is finite distance between any two points in space.

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6 minutes ago, vlaiv said:

No one mentioned boundary.

There is distinction between "bounded" geometry and one with boundary.

Bounded simply means finite in extent in sense that distance between any two points in space is less than some particular number associated with geometry. It does not imply boundary. Maybe best way to explain it would be 1d case.

Let's look at straight line that goes off to infinity. Now we are not considering "boundary" of such line with respect to higher dimensions that we embed geometry in - we don't think that line has boundary with respect to paper that it is draw on, nor in 2d/3d space that we imagine it in. We define boundary as place where one can't move further in given direction as there is no "next" point. With line we only have two directions - left and right or "up/down the line".

With straight line you can choose two points to be further away than any given distance. Line is unbounded in this sense.

Now let's consider circle with finite radius, again only directions are "up/down" the circle, or clockwise / anticlockwise. Again such geometry does not have a boundary, but it is bounded. Pick any two points on the circle and they will be closer than (2r+1)*pi where r is radius of this circle.

That is what bounded means - there is finite distance between any two points in space.

In which case, I repeat my statement using the term 'bounded'

I would say that adding a requirement that the Universe be bounded adds complexity. What does it even mean for a universe to be bounded?

There is no evidence for boundedness that we can observe - so surely that is where Occam's razor should be applied.

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1 minute ago, Gfamily said:

In which case, I repeat my statement using the term 'bounded'

I would say that adding a requirement that the Universe be bounded adds complexity. What does it even mean for a universe to be bounded?

There is no evidence for boundedness that we can observe - so surely that is where Occam's razor should be applied.

Alternative for bounded universe is universe with infinite spatial extent. We currently have no evidence one way or another, or rather evidence so far supports both, within measurement error.

My initial question was - why is there a priori assumption that universe is infinite in spatial extent, or rather most scientists believe it is - flat and unbounded, as this goes against what we might call common sense in so far as:

a) there are no infinities in nature - none that we have found so far

I would like to address last post by Andrew although it is likely that he won't be replying any more - I'm simply failing to see what sort of significance would limiting e value to finite sum produce in Bose Einstein and Fermi Dirac statistic except calculation error below experimental threshold.

I would also like to point out that definition of convergence in math might give a clue as to replacing infinite sum constant with corresponding finite series sum - which is based on finite limit where error can be made arbitrary small. This is also basis for numerical mathematics - or computation with certain precision.

b) universe with infinite spatial extent leads to whole bunch of multiverse ideas - which just complicate things - and here Occam's razor comes in - why do we need these additional things (well we don't need them, but they are byproduct).

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13 minutes ago, vlaiv said:

Alternative for bounded universe is universe with infinite spatial extent. We currently have no evidence one way or another, or rather evidence so far supports both, within measurement error.

My initial question was - why is there a priori assumption that universe is infinite in spatial extent, or rather most scientists believe it is - flat and unbounded, as this goes against what we might call common sense in so far as:

a) there are no infinities in nature - none that we have found so far

I would argue that there is no 'a priori' assumption, and given the absence of evidence, there is no reason to invent any bounding.

Come up with evidence and it may make be necessary to assume a boundedness, -but it needs more than a plea to 'common sense'.

I was checking the 'famous Einstein phrase', but it turns out he may not have said it; so instead I will quote Robert Oppenheimer

Quote

Common sense is not wrong in the view that is meaningful, appropriate and necessary to talk about the large objects of our daily experience…Common sense is wrong only if it insists that what is familiar must reappear in what is unfamiliar.

Edited by Gfamily

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9 hours ago, Gfamily said:

I would argue that there is no 'a priori' assumption, and given the absence of evidence, there is no reason to invent any bounding.

Come up with evidence and it may make be necessary to assume a boundedness, -but it needs more than a plea to 'common sense'.

I was checking the 'famous Einstein phrase', but it turns out he may not have said it; so instead I will quote Robert Oppenheimer

First of all - I agree with above quote - we can't tell universe how to behave, we can only asses what are the facts.

Let me just point out that positively curved finite / bounded universe is not just fringe / made up idea - it is one of the solutions of lambdaCDM cosmology - Einstein's GR equations. For omega>1 we get positively curved bounded geometry.

I can offer you another quote that will emphasize my point: "Extraordinary claims require extraordinary evidence".

To my mind, claim that something in the physical world is infinite is extraordinary claim. It's a bit like having hypothetical scenario where you have an equation that has multiple solutions and you choose to focus on one particular solution that violates conservation of energy. It would be justified to do that only in presence of very firm evidence that it is so.

Why did I use above comparison? I will draw a parallel on the fact that in all our experiments and all our observations we determined that energy is conserved. It is reasonable to assume it is one of the features of universe. We even made it into a law of nature - Thy energy will be conserved!

We in fact have not observed anything that is infinite in the universe - everything so far has been finite. We could have similarly coined a law of nature that goes like: It will be within bounds!

There might be a clue that flat / infinite solution is not the correct one? This of course does not imply that positively curved / finite universe is correct - we still have negatively curved hyperbolic universe. Also it might point out that we are missing something else in lambda CDM.

I'm talking about discrepancy between Hubble constant measurements. Direct observations place this value at about 73km/s/mpc. Observations that rely on lambdaCDM model where flat geometry is assumed (this still does not mean infinite universe - it could be flat and finite, although isotropy would suffer in this case) give results at about 67km/s/mpc.

With latest measurements error bars were significantly reduced and we now have great confidence that this is not due to random errors (I believe that it is now 1/10,000 for random error of measurement).

People have no clue why this might be so, and some of hypothesized answers to this problem assert that there might be additional component to mass/energy density - like dark matter interacting more strongly with light / regular matter than is currently believed. This would shift density parameter to higher value making it "more positive" - hence omega>1 or positively curved universe - or rather finite / bounded universe.

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19 hours ago, andrew s said:

Strange then that the two most successful physical theories Quantun Field Theory and General Relativity both are based on a continuous spacetime.

Regards Andrew

Quantum Field Theory by definition cannot be continuous.

Newton's theory of gravity has been more successful ( in use for longer and contributed more to science ) than this but was eventually proven to be incorrect .

Just because something is successful doesn't mean it is correct.

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20 hours ago, andrew s said:

Can you provide examples?

Regards Andrew

If the universe was infinite the sky would either be infinitely bright or the same brightness level overall ( there are 2 equally valid but disagreeing theories on this ) .

However both agree that the sky would be a uniform colour whatever its brightness.

There are no other sensible theories on this for an infinite universe , ( plenty of different theories for a finite one ).

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21 hours ago, vlaiv said:

a) there are no infinities in nature - none that we have found so far

Just a thought but dose the human brain or thought itself qualify...

Alan

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3 hours ago, Kev M said:

Quantum Field Theory by definition cannot be continuous.

I am sorry you are wrong. The space time of QFT is that of special relativity and is continuous. Some results from QFT ( e.g the spectrum of the hydrogen atom) are quantisied but not all (e.g. the position of a free particle).

Regards Andrew

Edited by andrew s

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2 hours ago, Kev M said:

If the universe was infinite the sky would either be infinitely bright or the same brightness level overall ( there are 2 equally valid but disagreeing theories on this ) .

However both agree that the sky would be a uniform colour whatever its brightness.

There are no other sensible theories on this for an infinite universe , ( plenty of different theories for a finite one ).

Wrong again. The universe is taken to be spatially infinite but has a finite age. This results in a finite observable universe which is expanding and circumvents Olber's Paradox. This is well known.

Regards Andrew

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15 minutes ago, andrew s said:

I am sorry you are wrong. The space time of QFT is that of special relativity and is continuous. Some results from QFT ( e.g the spectrum of the hydrogen atom) are quatisied but not all (e.g. the position of a free particle).

Regards Andrew

Doesn't that depend on scale i.e. Planck distance

Anyway, I've always thought the size of the universe must have similarities to the speed of light. So you can't accelerate up to the speed of light from a starting speed that's less than the speed of light since it would require an infinite amount of energy. Similarly, if the universe started off small (finite) and then expanded since the big bang, how could its size ever become infinite? It can become arbitrarily large else could actually have started off infinite in size. These are just my thoughts - I have not the maths to prove it!

Louise

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@vlaiv energy is not conserved in General Relativity. Both Einstein and Hilbert recognised this and  asked Emmy Noether to look at the problem and this led to her theorem which related conservation laws to symmetries.  Conservation of energy is related to time reversal symmetry.  This is broken in a curved spacetime.

Regards Andrew

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4 minutes ago, Thalestris24 said:

Doesn't that depend on scale i.e. Planck distance

Anyway, I've always thought the size of the universe must have similarities to the speed of light. So you can't accelerate up to the speed of light from a starting speed that's less than the speed of light since it would require an infinite amount of energy. Similarly, if the universe started off small (finite) and then expanded since the big bang, how could its size ever become infinite? It can become arbitrarily large else could actually have started off infinite in size. These are just my thoughts - I have not the maths to prove it!

Louise

No it does not. In pop science the Planck length is often seen as a limiting distance but in reality it is just a unit of length like the meter defined in terms of more fundamental constants.

The metrical expansion of the universe is of space not a material object and can and does exceed the speed of light.

In the flat LCMD model the universe has always been spatially infinite. Metrical expansion is a subtle idea as are ideas about infinity!

Regards Andrew

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21 minutes ago, andrew s said:

No it does not. In pop science the Planck length is often seen as a limiting distance but in reality it is just a unit of length like the meter defined in terms of more fundamental constants.

The metrical expansion of the universe is of space not a material object and can and does exceed the speed of light.

In the flat LCMD model the universe has always been spatially infinite. Metrical expansion is a subtle idea as are ideas about infinity!

Regards Andrew

Yeah, I appreciate space/spacetime can expand faster than light but that doesn't mean it would reach infinite size (extent?). Why would it expand to a size greater than it needs to be (to contain the matter within it) anyway? I just reckon it would be illogical (to quote Spock, ha ha). Conceptually I can't get my head around an infinite universe but can contemplate infinitely many of them i.e. a multiverse

Louise

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39 minutes ago, andrew s said:

@vlaiv energy is not conserved in General Relativity. Both Einstein and Hilbert recognised this and  asked Emmy Noether to look at the problem and this led to her theorem which related conservation laws to symmetries.  Conservation of energy is related to time reversal symmetry.  This is broken in a curved spacetime.

Regards Andrew

I new someone will pick up on that - but idea was to explain that we make things into law because of their omnipresence in experiments and observations and to draw a parallel to absent infinities. Not in a sense that something is strict law, but rather that we prioritize assumptions that go in line with our knowledge so far and that there must be solid evidence and understanding if something is to the contrary.

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5 minutes ago, Thalestris24 said:

Yeah, I appreciate space/spacetime can expand faster than light but that doesn't mean it would reach infinite size (extent?). Why would it expand to a size greater than it needs to be (to contain the matter within it) anyway? I just reckon it would be illogical (to quote Spock, ha ha). Conceptually I can't get my head around an infinite universe but can contemplate infinitely many of them i.e. a multiverse

Louise

I am sure I read or saw something that suggested that at or just after the big bang that particles did exceed the speed of light and are still doing so since they have not had to accelerate up to it. Another observation in a science documentary was that the speed of light is slowing so is not a constant.

Alan

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3 minutes ago, Thalestris24 said:

Yeah, I appreciate space/spacetime can expand faster than light but that doesn't mean it would reach infinite size (extent?). Why would it expand to a size greater than it needs to be (to contain the matter within it) anyway? I just reckon it would be illogical (to quote Spock, ha ha). Conceptually I can't get my head around an infinite universe but can contemplate infinitely many of them i.e. a multiverse

Louise

We can't tell what initial conditions were no more than we can now conclude if universe is indeed infinite or bounded. These two go inline - infinite universe as initial condition will give rise to infinite universe now, no matter expansion rate - same goes for bounded / finite universe - no matter how much of expansion there was so far - if it is limited in speed of change of scale factor (equivalent to finite speed of expansion at any one time) - it will still be finite / bounded universe after finite amount of time.

Shape of universe that we are discussing (primarily) here is tied to bending of space time. If density of matter / energy is such that space is "curved back on itself" - it will be positively curved and thus of finite extent - bounded. Image that may help with thinking about this is "inside of black hole" - nothing can escape and if we omit (I need to be strict now with explanations ) Hawking radiation and fact that there is something on the outside, mathematical singularity and such and concentrate on simplistic behavior - any light trying to "escape" black hole will "curve" back and end up again in black hole - it can never leave. As we know light follows "straight lines" in curved space time - so positively curved space means that if you follow a straight line in any direction you will end up where you started coming from opposite direction.

Flat universe is just regular 3d space that we are used to - Euclidean space - if you start at the point and follow a straight line - you will end up in "infinity".

Negatively curved space is pretty much the same in sense of infinity - but has other properties like angles in triangle add to less than 180 degrees and further things are they appear larger than they would in "regular" space.

Yes, infinity just means true mathematical infinity - meaning that spatial extent of universe never ends in any direction nor can you reach your origin by going in any direction, there is infinite amount of "stuff" in such universe and infinite number of interactions are taking place - in fact all possibilities happen all the time at some points - because space is infinite and there is "enough room for everything" - and then some.

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Apparently, there may be no objective reality anyway. There certainly won't be any for me after I've died, so being a bit of a nihilist, nothing really matters, no even matter itself ha ha.

Louise

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On 21/05/2019 at 22:53, andrew s said:

So what about the key constants pi, e which are transcendental with an infinite number of digits.  Is the area of a unit circle not real? Is it truncated as there are more digits in pi than atoms in the observable universe?

Regards Andrew

The language we use to define the circle (mathematics) produces what we define as infinity. Infinity is a consequence of that language it does not follow it exits in nature.

Jim

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Oh I need to correct myself before someone spots the mistake and quotes me on it

24 minutes ago, vlaiv said:

and further things are they appear larger than they would in "regular" space.

In fact in positively curved space things that are further from us appear larger than they would in flat space and in hyperbolic space - smaller than they would in flat one.

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By the way I don't know if the Universe is spatially flat or not and is as @vlaiv proposes. All I am trying to do is explain as best I can what the current consensus view is within science community.

My understanding is that the best current data indicates that it has a simple topology and is very close to flat. We could as @vlaiv proposes be mistaken and that it is curved and we are making the same mistake as the original flat earth proponents did.

However, it is so close to flat that within the currently observable universe we cannot tell the difference so the current working hypothesis is that it is flat. This makes some calculations simpler!

Concerns about the I application of if being infinite if true or not are all outside the obsevable universe so it hardly matters if the are real or not -reather a  matter of taste.

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1 hour ago, Thalestris24 said:

Similarly, if the universe started off small (finite) and then expanded since the big bang, how could its size ever become infinite? It can become arbitrarily large else could actually have started off infinite in size. These are just my thoughts - I have not the maths to prove it!

Louise

And that is the problem I have with the concept of infinity. The universe at it's beginning no matter how small or large was by definition infinite as it held everything. As that universe expanded it retained its infinite crown as by definition it contained everything.  So infinity is not absolute , there are many versions of infinity.  I go back to what I said before, I believe it's a mathematical construct resulting from our language mathematics.  A curious artefact.

Jim

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2 minutes ago, andrew s said:

By the way I don't know if the Universe is spatially flat or not and is as @vlaiv proposes. All I am trying to do is explain as best I can what the current consensus view is within science community.

My understanding is that the best current data indicates that it has a simple topology and is very close to flat. We could as @vlaiv proposes be mistaken and that it is curved and we are making the same mistake as the original flat earth proponents did.

However, it is so close to flat that within the currently observable universe we cannot tell the difference so the current working hypothesis is that it is flat. This makes some calculations simpler!

Concerns about the I application of if being infinite if true or not are all outside the obsevable universe so it hardly matters if the are real or not -reather a  matter of taste.

Actually, I started this thread in search of answer to the question - why do we assume it is infinite in lack of solid evidence. In fact we do not assume that in principle - and as you've said - current data points to near flatness or large curvature radius in case of curved space, and indeed that is a tricky one - you can never measure something to be precisely 0 as there will always be some uncertainty in measurement.

It does however seem to be prevailing opinion that universe is indeed infinite (of flat variety) - if it were not so, there would not be many follow up ideas (verifiable or not), like multiverse. It is actually intriguing to me how easily we accepted notion of infinity related to the physical world.

It is probably related to mathematics apparatus that we use to describe and formulate our theories. It is easy to forget that we are always working with approximations at best. Good examples are both often used constants, and like you pointed out both GR and QFT are based on continuous space-time.

This of course does not mean that these models are 100% true and that our laws need exact pi or e values to be 100% correct. In fact I'm positive that no one ever used exact pi or e value in any of their calculations, ever, let alone in experiments where our theories were confirmed to very high precision. I suspect that same is true for our model of continuous space-time. Regardless of true nature of it, mathematical model we use works extremely well so far, however similar model based on finite distances with "enough granulation" would also work to the same level of empirical precision. Usage of one model over another is matter of convenience rather than proof of underlying reality.

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18 minutes ago, saac said:

The language we use to define the circle (mathematics) produces what we define as infinity. Infinity is a consequence of that language it does not follow it exits in nature.

Jim

This asks the question "is there a better way" than our concept of mathematics, nature produces circles (not very good ones most of the time) and plenty of other regular shapes with very few apparent rules....

Alan

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7 minutes ago, saac said:

And that is the problem I have with the concept of infinity. The universe at it's beginning no matter how small or large was by definition infinite as it held everything. As that universe expanded it retained its infinite crown as by definition it contained everything.  So infinity is not absolute , there are many versions of infinity.  I go back to what I said before, I believe it's a mathematical construct resulting from our language mathematics.  A curious artefact.

Jim

You have to be careful about usage of word infinite. One that contains "everything that exists" is not necessarily infinite. Infinite that we are talking about has very exact meaning and is related to concept of geometry of space. If for any given number, no matter how large you select it to be, you can find two points in space that have separation greater than that number in your chosen units - then universe is infinite in size.

Infinite universe in above sense has infinite amount of "stuff" in it if we assume homogeneity, or if we assume that density is finite number.

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